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Sunday, April 06, 2008

Models and Theories

Words can lead to misunderstandings in the communication of science if their scientific usage has a meaning other than the colloquial one. Examples for this are abundant, like the words 'significant' (see 'Statistical Significance' ), 'optimal' (see 'Optimum'), or 'simple' (see 'Simple Lie Group').

"Model" and "theory" are both words that physicists use frequently, and often with a different meaning than attached to it in the colloquial language. Since we on this blog write about models and theories all the time, I thought it worthwhile to clarify what I mean with that.

Disclaimer: This isn't meant to be a definition, just a clarification. As with all language related issues there is a large grayscale to a word's applicability. I am not claiming the following is a standard for usage-of-words.I. The Real World Out There

If you are one of our frequent readers then you know that I occasionally feature the idea that all of our commenters are actually manifestations of my multiple personality disorder. Let me call that a 'theory' to describe my 'observation' of comments. It's not scientifically a particularly compelling theory. For one, some commenters have shown up in my office which means to make my theory viable, I should add some numbers to my ICD-10 diagnosis , like F22 (Delusional Disorder) or F44.1 (Dissociative fugue). Alternatively, I could simply argue there is no reality other than what the neurons in my brain produce. That's a theory as well, and since I can never falsify it, it's not something a scientist should spend much time on.

To begin with, it is therefore for practical purposes reasonable to consider the possibility there is something like a "real world out there"[1], including my computer, you, and the CMB radiation - and it's this real world out there that we are trying to understand and describe.

For example, you could speculate that your phone always rings if you take a bath. There is reality out there: you, the bathtub, the phone. To make a theory out of your speculation - call it a 'hypothesis' because it sounds better - you need to do somthing more. To begin with your hypothesis isn't very useful because it's too unspecific. You would want e.g. to add that the phone is switched on. Also, some quantification of your framework is necessary. If you just say the phone will ring, you can shrivel in your bath until you die out of boredom, and never falsify your hypothesis because it could always ring the next minute [2]. Instead, to make your theory credible you would want to clarify "If my phone is turned on, it will ring within 10 minutes after I sat down in a bathtub full of water".

Now consider you do that, but the phone doesn't ring. Then there is always the temptation to add more specifications a posteriori. Like, it only happens on Wednesdays, and only if you use rosemary scented bubble bath, and only if you have large enough extra dimensions. Or so. You can add a long series of 'only ifs' to explain a negative outcome of your experiment. That's still a theory, but with each 'only if' it loses some of its generality, and its applicability becomes more and more limited, which makes it less and less interesting.

II. Theories and their Limitations

What scientists usually mean by theory is a testable hypothesis about an important aspect of the real world out there that has predictable power, and a consistent and well-defined framework.

- 'Testable' means, there is a possibility to prove it false. Unless you have a theory of very limited applicability, you can never verify it to hold in all possible circumstances, for all experiments that will ever be done, by anyone. However, for your theory to be good for something it must at least be possible to falsify it, otherwise it's like claiming you have this invisible friend who is so smart nobody can ever prove he is really there because he's shy and just doesn't want to.

- 'Predictable power' means your theory tells you what will happen under certain circumstances stated in your theory - in physics this usually means prediction of experimental data. Experimental data can also be already available, and await to be explained by a theory. Though one better shouldn't call that a prediction, maybe a 'postdiction'. The possibility for experiments that can be done to confirm a theory differs greatly between the fields. For example, we can't repeat the evolution of species with slightly different initial conditions. Natural Selection such is somewhat weak on the side of useful predictions, but it does a good job explaining the evolution of species that archaeologists find documented. In physics we today have a lot of experimental data, like e.g. dark energy and dark matter, that yells at us theorists because it wants to be explained.

- 'Well-defined framework' means your theory is in a comprehensible form, and not a big pile of glibber that one can't grab because the interpretation is unclear. Roughly speaking, if one can't understand and apply a theory without consulting its creator, it's not a scientific theory.

- 'Important aspect' is very subjective. I'd think your bathtub theory for example isn't so tremendously important for the biggest part of the world, and wouldn't qualify as a 'scientific theory'. But at which stage scientists are inclined to promote a hypothesis to a scientific theory depends very much on the circumstances.

One can have a lot of theories. Theories that become accepted scientific knowledge are those that are experimentally well confirmed and have proved useful. The point about Natural Selection is not that it is a theory but that it is a very well confirmed theory with explanatory power. The point about Einstein's theory of General Relativity is not that it is a theory, but that it is a theory confirmed to very high precision with a large number of experiments. The theory of the luminiferous aether on the other hand is a theory as well, but one that was proved wrong with the experiment by Michelson and Morley [3]. String theory, as well as other approaches to quantum gravity, are difficult cases because they would become important in energy ranges far outside the reach of experiments on earth, so their status is pending.

Theories are reliable typically in a limited range and up to a certain precision. Special Relativity for example reaches its limits when the curvature of space-time becomes important, in which case one has to use General Relativity. Your bath tub theory reaches its limits at a temperature of 100°C at which you'd get problems filling the tub, not to mention getting in.

If somebody proposes a new theory it is most often an improvement of an already existing one, either because it applies with larger generality, to better precision, or both. Still, the 'older' theory might remain useful. For example, the non-relativistic limit is accurate to very high precision for slowly moving objects and using the fully relativistic framework is often an unnecessary overkill.III. Models

Okay, so far we have the real world out there, and we have a theory. Theories are usually very general concepts from which one constructs a specific model. The model is a simplified version of the real world out there, simplified in the sense that it deals only with a limited amount of details. For example if you want to compute how a cow drops out of a plane, you can forget about her milk-efficiency, and assume to good precision it is a ball, with a mass M and a radius R. You can also attempt to understand a political arguments by the gender of its proponent. This identification of features is a model, underlying which there is your theory that you want to test.

In physics, we have for example the quantum field theories which underlie the Standard Model of particle physics. In this model, we identify particles with states in the Fock space, observables with expectation values, and particle properties with gauge charges that belong to specific gauge groups. Another example is the ΛCDM model in Cosmology, underlying which is Einstein's theory of General Relativity. The identification of the relevant ingredients to the model is crucial to make it useful.

Besides the identification of objects, typically your model will need to use some data as an input to make predictions for further data. In other words, it will have free parameters that the theory can not predict and that just have to be measured. Einstein's theory of Special Relativity for example has a constant that you can show to be the speed of massless particles. Then you go and measure this constant, commonly known as c, with which you can then apply your model to other cases. The more free parameters a model has, the less useful - not to mention, ugly - it is. A model that needs the same amount of parameters as there is data to fit isn't good for anything. There is always a n-th order polynomial which lies exactly on n data points.

Theories and models can come in many different forms. In physics our models use the language of mathematics, and our theories tell us how to identify mathematical quantities with 'real' physical objects. Models can also be computational, in which case you translate the real world into input of your computer code. But in other areas, mathematics or computation is not necessarily the language of choice. For example, in psychology one has the 'Existential Theory' which in a nutshell says humans are driven by four existential fears: death, freedom, isolation, and meaninglessness. Based on this theory, one can then try to understand a patient's problem, i.e. build a model to explain the real world out there. In this case, mathematics isn't the language of choice, mostly because it is too inflexible to cope with something as complex as human behaviour. Another example is Adam Smith's "Wealth of the Nations", which puts forward the 'theory' of the invisible hand. The tragedy with this specific example is that even though this theory is known to be wrong or not applicable in many cases, it is an argument still used that influences the lives of people all over the world.

The example from psychology also illuminates another feature of a good model. I am not much of a psychologist, but even to me the reduction of human behaviour to four existential fears seems to be overly simplistic. And it probably is, but what makes a useful theory is that after stripping off lots of details you have identified some relevant properties that can lead to an improved understanding, even though restrictions may apply.

However, a model doesn't necessarily have to be about describing the real world out there. To achieve a better understanding about a framework, it is often helpful to examine very simplified models even though one knows these do not describe reality. Such a model is called a 'toy-model'. Examples are e.g. neutrino oscillations with only two flavors (even though we know there are at least three), gravity in 2 spatial dimensions (even though we know there are at least three), and the φ4 theory - where we reach the limits of my language theory, because according to what I said previously it should be a φ4 model (it falls into the domain of quantum field theory).

IV. Theoretical Physics

A big challenge especially in theoretical physics is that theories potentially remain untestable for a long period of time, because the farther our theories depart from every day experience, the more effort we have to make to design suitable experiments. In these cases, internal consistency is often the only guide. Quantizing gravity for example is actually not the problem. You can quantize it if you want to. The problem is that the outcome is nonsensical. This way, one can drop a lot of theoretical approaches even without testing them on the real world. It is for this reason that apparent paradoxa appearing within a theory receive a lot of attention, as their investigation and solution can be the source of new insights and progress.

Besides consistency, some people also like to call upon more ethereal values like 'beauty', 'elegance' or 'naturalness' to argue for the appeal of their theory. It is a slippery slope however, as the relevance of these factors is a theory in itself, and not a scientifically well confirmed one.

You could for example have the theory that the real world is made out of tiny vibrating strings. Once you've made sure your theory is internally consistent, and added sufficient 'only ifs', the way to proceed is then to build a model, make a prediction, and line up for the Nobel Price. Alternatively, you could have the theory that the real world is made out of braids, and identify particle properties with braiding patterns. However, if your model doesn't reproduce gauge fields we commonly call photons and gluons, it doesn't seem to describe the real world out there, so it is at utmost a toy model. You can have all sorts of theories. Like you will be reborn as a Boltzmann brain. The value of such theories differs greatly depending on its usefulness.

Such, in theoretical physics you make a living with speculation, with the eternal hope that you manage to catch a glimpse of Nature's ways and experiment will confirm you. It is a difficult task, since every new theory first needs to reproduce all the achievements of the already established ones, plus it needs to lead to new insights. The requirement of consistency is one that people not working in the field typically underestimate - it greatly reduces the amount of freedom we have with our speculation. In a certain way it is as fascinating as frustrating if a theory you have disagrees with you and just doesn't do as you want it to. I am always annoyed by this. It's like I think if I made it, it's supposed to do what I want. Very possibly for this reason I am inclined to say that we don't actually invent theories, but that we discover them.

Another challenge in this procedure is the problem that different theories can under certain circumstances result in the same model. In such cases, one has to look for scenarios in which one can distinguish both theories. If there are none, one can call both theories equivalent, and the difference is one of interpretation. Though without any direct consequences as far as predictions are concerned, establishing an equivalence between two interpretations and a change in perspective can be very fruitful for further developments.

IV. Summary

A scientific theory is a consistent and well-defined framework to test a falsifiable hypothesis about the real world out there. A theory that becomes accepted knowledge is one that has been confirmed to high accuracy, and has proved useful. Theories underlie the models that we use to describe the world. We can also investigate 'toy models' to understand our theoretical framework better, even though the scenario is not realistic. Internal consistency is a strong requirement on a scientific theory that is often underestimated.

Post Scriptum

After finishing this writing, I find that my above explanation disagrees with other's. For example Laurence Moran explains:

"A theory is a general explanation of particular phenomena that has withstood many attempts to disprove it. Because of the evidence supporting the explanation and because it hasn't been refuted, a theory will be widely accepted as provisionally correct within the science community."

As I said previously, arguing about words isn't something I like to engage in, but this would mean that there are no falsified theories, and it constrains the usage of the word 'theory' to those theories that are 'correct' descriptions of nature (to some degree) because there is already evidence supporting them. Though possibly I misunderstand, and he means to say that the science community will generally only call something a 'theory' if it lives up to certain quality standards, withstands the most obvious criticism, and the possibility exists that it describes the real world out there. (Like e.g. if your 'theory' does not have fermions, forget about it.)

"Some scientific explanations are so well established that no new evidence is likely to alter them. The explanation becomes a scientific theory. In everyday language a theory means a hunch or speculation. Not so in science. In science, the word theory refers to a comprehensive explanation of an important feature of nature that is supported by many facts gathered over time. Theories also allow scientists to make predictions about as yet unobserved phenomena."

Which I think goes well with what I wrote above.

[1] The phrase "The real world out there" is borrowed from Lee's book, who I believe borrowed from elsewhere, but I can currently neither recall the actual origin, nor where I put to book. Sorry about that.[2] One finds an iteration of this sort of theory that is unfalsifiable within the experimenter's lifetime in Hollywood. It's called the 'One day I will be rich and famous' theory of the unknown actor. Surely fame is just around the corner, hang on for one more day.[3] The aether theory however seems to have Zombie character and occasionally comes back to haunt us in various alterations that escape the constraints of Michelson-Morley.

54 comments:

Bee, good writing and a good rundown of the basic structure and application of concepts for theory and proof in science. One of the big recent controversies of course is how much latitude and agreement to give theorists who speculate about things that we can't easily study experimentally (at least with what we have available or can do in practice.) String theory has become a focus of tension over this issue.

Another interesting factor, not much discussed in "paradigmatic" discussions is the presumed legitimacy of "toy model" simulations. An example would be "this is how EM radiation would propagate if space had five space-time dimensions," etc. Another might be, what kind of "other universes" wormholes etc. connect to, even if we can't get through to them (BTW, I haven't noticed as much about "other universes" in the strict GR context, like I used to. How come?) Well, we can't usually do a physical experiment, but people assume certain things and do models anyway. (I talk about consequences of such an extrapolation in one of my blog posts.) A look at the literature of such model explorations shows how little phased most scientists are by not being able to do a literal experiment on them. They seem to take as meaningful the counterfactual conditional, "If the fine-structure constant was x instead of what it is, then ..." I'm OK with that, but it isn't strictly falsifiable. It is per the math of plugging in variables, but not "literally" per "experiments."

Finally, there is the accommodation made to needing a concept even if it isn't strictly falsifiable, etc. Note that probability claims are rather weird in that no outcome can be used as a test for "falsifiability" - if you pick 100 or even 200 heads in a row to "show" that a coin wasn't a fair coin, then eventually even a fair coin would fail the test and etc. And what meaning is there to, the probability changes with time versus the variations in outcome under a "constant" probability? Probability has to be played by ear, combined with theoretical justifications, etc. We draw a line in the sand at X confidence level and say we'll believe it even though it might still be a coincidence, etc.

In short, the real task is messy and can't be reduced to a positivistic "fundamentalism" any more than "market fundamentalism" is good for economics or the operating economy.

Aha! if the initial hopes of string theory uniqueness had worked out, then The String Theory would lead inexorably to the One and Only String Model, and theory and model would be indistinguishable. In general, it seems to be an expectation of physicists today that the final Theory of Everything is also the unique Model of Everything.

Since LQG cannot do that (be the unique Model of Everything) it was sneered at (among other reasons).

Ironically, string theory itself does not contain any useful models of Everything. It does contain other useful models, e.g, of blackholes.

-- it would also seem that in general, it is models that make contact with experiment, not theories.

-- i'm trying to think of cases where we have no theory, only models. Certainly in biology, (e.g., models but not theories of malignancy?) but in physics? General phenomenological laws might be called models? E.g., Tully-Fisher law for galaxies?

-- the theory of evolution itself is never directly verified; rather it unifies what would be a very large number of models.

Glad you like the post. I agree, the real task is as usually more messy than it sounds. To use a quotation that I liked very much (and which I mentioned earlier):

"Learning about modeling is a lot like learning about sex: despite its importance, most people do not want to discuss it, and no matter how much you read about it, it just doesn't seem the same when you actually get around to doing it." ~ John H. Miller and Scott E. Page in Complex Adaptive Systems

That is to say, in practice the situation is rarely entirely black or white, but a spectrum of colors that have to be sorted out. For example, whether or not an approach is consistent might not be immediately clear. It can take a while to figure it out. Or maybe a problem can be overcome with more investigation, then the question is how much 'more' time and energy does one want to invest before giving up?

As to the toy-models, to me they serve two different purposes. For one, it's like having a look at an artist's study. Not yet the full picture, but an investigation of the relevant details. It is often useful for didactical reasons to have these studies available. The other point is one of collaboration. Unfortunately, we all work under the pressure to 'produce'. A toy-model that points out potentially interesting features of an approach can serve as an offer for others to look into the details.

As to the string theory discussion, much of it I think is inappropriate. The problem that theoretical physicists speculate about things that are potentially not easily experimentally testable is not one of string theory alone. As I expressed in my post above, I don't find it too surprising that the more we learn about nature, the more difficult it becomes to test a theory. What concerns me about this whole discussion much more is not the string community specifically, but that the way the discussion takes place shows that the research in our community is influenced by political, sociological, and economical factors which biases opinions - ours as well as those of the public - on research topics. I think this is a very bad state, and one should be concerned about it. That being said, I'd say there is trouble, but no crisis - at least not yet.

Yeah, I would say in general it's the model that actually makes the contact with experiment, not the underlying theory. I find the whole idea of a 'Theory of Everything' an overstatement, but indeed when I wrote the paragraph about the models I had the same thought, namely that there is an expectation that a 'Theory' of everything would bring it's 'Model' along. I don't know whether this will ever be possible. I doubt anybody knows. I personally think that whatever we do, we will always be left with some question of the sort: but why these (gauge groups, masses, numbers of generations, dimensions, parameters in the standard model, cosmological parameters, etc etc). Best,

I'm afraid we already have one. I don't want science to be run based on the prevailing believe that the a capitalistic, competetion driven system will optimize how people spend their time and energy, lead and directed by an 'invisible hand'.

The theory of the luminiferous aether on the other hand is a theory as well, but one that was proved wrong with the experiment by Michelson and Morley [3].

The Wikipedia page you link as ref [3] states:

... A possible explanation was found in the Fitzgerald–Lorentz contraction, also simply called length contraction. According to this hypothesis all objects physically contract along the line of motion (originally thought to be relative to the aether), so while the light may indeed transit slower on that arm, it also ends up travelling a shorter distance that exactly cancels out the drift. In 1932 the Kennedy–Thorndike experiment modified the Michelson–Morley experiment by making the path lengths of the split beam unequal, with one arm being very short. In this version a change of the velocity of the earth would still result in a fringe shift except if also the predicted time dilation is correct. Once again, no effect was seen, which they presented as evidence for both length contraction and time dilation, both key effects of relativity.

Ernst Mach was among the first physicists to suggest that the experiment actually amounted to a disproof of the aether theory. ...

I've never seen a clear explanation as to how the Michelson-Morley experiment disproves the aether, it's more a case that the Michelson-Morley experiment has to be interpreted with the false assumption that there is no length contraction, in order to get rid of the aether.

Empirically, there is length contraction, and there is evidence in general relativity for a differential geometry (or a spacetime fabric manifold) that gets curved by the presence of mass, etc. But Einstein's relativity, both special and general, is classical physics. It doesn't involve quantized fields.

As soon as you start looking at spacetime as involving quantized gravity fields, with gravitons and other field quanta being exchanged between particles to produce forces, the whole concept of the universe being based on classical differential geometry evaporates.

Now, what effects will occur if an atom moves into a quantized gravity field? If it's going to be running into a graviton field, it's going to encounter graviton impacts more frequently in the direction of motion than in other directions like someone running in the rain, so will that type of effect distort a moving particle's shape and flatten it? Clearly, general relativity tells us a bit about the correct way to model such fields as a while: the source term for the gravitational field is best modelled by analogy to a perfect, frictionless, fluid.

It seems that since the field quanta, gravitons, require a velocity c to carry the gravitational field at the correct velocity to match empirically confirmed predictions of general relativity, the various effects on a atom trying to move in such a graviton populated field will depend on the ratio of the velocity of the atom, v, to the velocity c. The Lorentz-FitzGerald factor [1-(v/c)^2]^0.5 models the physical effects from the space time fabric on moving matter, such as slowing down internal motions and contracting the length in the direction of motion.

The reason why Einstein's 2 posulates became popular in place of the contraction and time-dilation generating aether of FitzGerald (1889) and Lorentz (1893), is that there was a "cosmic landscape" of 200 versions of the aether theory (according to Eddington's 1920 book, Space, Time and Gravitation), and no experimental way to pick out the correct aether (if any of those models in the known landscape was correct).

However, since the advent of the Standard Model, there is some evidence for the kind of theory describing the general nature of force fields in the vacuum: gauge theories of the Abelian and Yang-Mills variety. This gives a model of the general type of process involves in generating forces: gauge bosons (field quanta) are exchanged between charges.

So there is now more hope that progress could be made towards picking out a physical model of the vacuum that could be experimentally validated.

Mach was the guy who claimed that atoms were pseudoscience, just because he had never laid eyes on one. This kind of proud hostility against admittedly unfashionable "crackpottery" sent Boltzmann over the edge.

Excessive rigor in science is as harmful as excessive open-mindedness. There are lots of real cranks out there who are wrong because they don't like the big bang theory, so they claim that the experimental evidence for it is inadequate, or they make up some false claim that that it is based on shoddy evidence.

Because they're being excessively critical, wrongly they believe they're being extremely scientific. The problem they have is that they don't have an alternative idea that is as simple as the big bang, and makes as many or more accurate predictions. So they're the crackpots, not those working on the big bang theory.

In the case of special relativity, you drive some equations based on two postulates. Fine, no problem. What goes wrong is if you try to claim that you've disproved aether because of the fact you can derive the 1889 aether theory formulae of FitzGerald and Lorentz from Einstein's two postulates that don't involve aether.

There are many other examples of cases where it is possible to derive accurate formulae with different arguments, using different assumptions in mathematical physics. If there is no difference between the results, you can't arbitrarily argue that one method of deriving the equations is wrong and another is correct.

They may all be right within the realm of validity of the assumptions made. If one method of derivation is ultimately wrong, it might not be the one you think is wrong based on what the consensus of fashionable opinion is.

Of course, it mainly depends upon usage – but generally, "model" is the most inclusive term.

We use language and symbols to fashion our sensory perceptions of 'reality' into models that we hope will communicate something about their meaning. Models are always, to some degree, "incomplete", sketches or heuristics.

Models include ideas, speculations, hypotheses, theories and laws of nature.

Within science, although "law of nature" 'always' should imply a very high degree of empirical confirmation, the others may – or may not.

"For example, whether or not an approach is consistent might not be immediately clear. It can take a while to figure it out. Or maybe a problem can be overcome with more investigation, then the question is how much 'more' time and energy does one want to invest before giving up? "

1. I read Lee's book with interest. I am a theoretical layman with an interst in stuff too heavy to understand. 2. "Phone rings when in bathtub" theory is dependent on Murphy's law being consistent and correct. I have actually seen instances when something could go wrong, but didn't.3. Do you know what lee is up to these days? Seems he's no longer with P.I.

Uncle Al said: "Since I can never falsify it, it's not something a scientist should spend much time on. You just killed string theory. Naughty girl."

No, string theory could in principle be falsified - we just don't have access to the necessary experimental equipment. Hence, string theory is part of science.

On the other hand, multiverse theories cannot be falsified even in principle (we cannot obtain evidence which resides in other parallel universes), so does that mean that multiverse theories should not be considered part of science?

A truly interesting topic, about a subject that I have pondered myself for many years. As you are aware I am not a scientist of any description and yet have had an interest in it for as long as I can remember. Some of my thoughts run parallel to your own particularly in what constitutes to be a theory. There has always been the central definition of what a theory should serve to be, as expressed by Newton in a statement he made at the end of his “Principia Mathematica” as follows:

“But hitherto I have not been able to discover the cause of those properties of gravity from phænomena, and I frame no hypotheses; for whatever is not deduced from the phænomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phænomena, and afterwards rendered general by induction.”

Now if one substitutes the word “gravity” with “natural phenomena” to generalize it, one comes up with what I consider a theory should be minimally limited to be as to what is for a required to do. I find much of modern physics has stepped well beyond this requirement; for they are in some sense seeking phenomena that doesn’t need to be explained, since it is not observed. If the current central mystery today is how GR and QM mes;, to assume that we must go to smaller structure levels then currently recognized, is more of an assumption then a requirement.

Now if you take the whole question of what physics serves ultimately to be, there are two general viewpoints that have been expressed in two quotes, the first by Lisa Randal in an interview a few years back when she said:

”Science is not religion. We're not going to be able to answer the "why" questions. But when you put together all of what we know about the universe, it fits together amazingly well.”

Here Dr. Randal is basically saying we have a machine that we need to discover all its parts and functions and yet without asking if it has or not an ultimate function. Something equivalent to someone discovering an automobile and learning how it works, without once considering what it might have been used for if anything.

Then you have Einstein’s view, which I am always hesitant to quote, since it is often misused to have people believe he was some sort of a religious fanatic yet of course wasn’t. That statement was of course as follows:

“I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts; the rest are details.

Now if one just replaces “God” with “nature” in the most generic sense, one will roughly arrive at what Einstein generally meant. That is for him, a theory was not so much to explain the bits and pieces, yet rather to explain why all the bits and pieces are as they are. If the purpose and aim of science is considered at this level, then both Newton’s and Dr. Randal’s expectations fall somewhat short. As I am not a scientist, it is not up to me to decide what that should be. However, I do know which one I prefer and that is Einstein’s. The other I think simply sells science short as to both its abilities and ultimate utility.

As to how a good theory should be recognized and decided to be one, I do not like Occam’s razor (which so many settle for) yet Einstein’s version which is:

"The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience"

Anonymous:I admit that it was sloppy of me to mention a theory without explicitly stating it's content and naming all assumptions, but then this threat isn't about the luminiferous eather. As I wrote above, if you add sufficient a posteriori assumptions, then you can always make your theory compatible with experiment. If it agrees with Special Relativity in all cases, then I don't care how you call it, but I would call it Special Relativity. If it doesn't, point out the difference, go measure it, and falsify one of both. Your speculation about the vacuum in quantum gravity is neither new nor original. Best,

Thanks. It is good to know that you have a different perception how the word 'model' is used, but it doesn't seem to overlap with mine. The way I see the word 'model' used in theoretical physics it is a construction within the framework of an underlying theory. You wouldn't use it for the theory itself. I had some examples in the text above, like quantum field theories, Yang-Mills theories, etc. You wouldn't call that a model. To get a model, you need to identify some of the constituents of the theory with objects in the real world. Like e.g. done in the Standard Model of particle physics. Best,

Dear Arun,Yeah, I think we're missing both a theory and a model of measurement in QM, measurement is just an element of the theory itself, but there's no theory for it. The problem here I'd say is what 'details' can you leave out? Does the detector matter? Does the experimenter matter? Does the rest of the universe matter? Best,

At the most fundamental intellectual level, the "construction within the framework" of the perception of even our most primitive observations are models – upon which all other models are built.

In everyday usage, a model is an incomplete representation of a "real thing".

We can only communicate 'sketches' of our perceptions of reality. So all of those (ideas, hypotheses, theories, etc.) are models.

Physics theories may be elegant and self-consistent mathematical theorems in which the variables represent physical parameters. But that isn't the character of all physical theories. Yet they're all trying to model 'reality'.

I think this definition is perfectly consistent with its use in physics.

This use of "model" also is a helpful reminder that science is just an ongoing, back-and-forth project, constantly striving to refine forever incomplete models, and then checking with how much confidence they seem to 'fit reality'.

I think we're talking past each other. What I'm saying is that e.g. 'quantum field theory' per se, as a recipe, is not a description of reality, and thus I wouldn't call it a model. It's just not sufficiently specified and doesn't make any predictions about about the real world out there - it's not even a 'sketch'. You will have to add more details, like what type of matter fields, how many, which gauge charges, masses and so on, to get a model. You can also make up something, which gives you a 'toy-model', as mentioned above. Also, physical theories are not mathematical theorems, this would imply they follow from something. Best,

There is a considerable technical literature on what a "theory" is in the Methodology of Science, a specialty in Philosophy of Science. IMHO, philosophers have demonstrated that the idea that a theory can be either verified or falsified is absolutely problematic. To even think of the relationship between the mathematics of a Physical theory and the real world as possibly a question of simply true or false is arguably a category mistake.

In formal approaches, a model is essentially a specialization of a theory, which could be as simple as adding one more axiom, but typically adds real-world details of an experiment. Such details should in principle be formulated as axioms, but generally are not, and are certainly not given the same status as the axioms of the theory. That is, an experiment that gives different results than a model is taken to invalidate the low status assumptions, not the whole mathematical structure -- unless it can be proved that there is no possible model of a theory that corresponds in an acceptable way with the phenomena.

A look at Imre Lakatos's approach to models is worthwhile, particularly for his idea of "bridge principles" between Physical theories/models and the real world. A more modern approach that is almost always received badly by scientists is the idea of "models as mediators" (there is a collection of articles with that title, edited by Morgan (no relation) & Morrison) between people and the world, which, broadly, supposes that models are the only way we have to talk about the world. For a really red rag, look at Nancy Cartwright's "How the Laws of Physics Lie", which is a great title.

There are various physicists technical ways of using the word "model", there are various popular ways of using it, and there are various Philosophy of Science technical ways of using it. The Physicists' way is largely grounded in the positivist philosophy of the 1920s-1950s, although some of the post-positivist critique of positivist methodology of science has made its way into common Physicists' ways of thinking.

Philosophers' critiques of scientists' practices are uncomfortable to hear, so they are generally ignored or belittled by scientists as too far from the realities of science. Appropriations committees are often more knowledgeable about Kuhn and Feyerabend than scientists are. IMHO, Scientists failing to understand and engage with post-positivist critiques, which have substantial elements that cannot be easily dismissed, is a large part of the modern funding crisis for science.

This is of course a throw away discussion of theories and models. The philosophical literature on scientific and physical models is voluminous. Philosophers have something too much of a love for quibbling about words.

As some commenters have noted, and you also in the addendum to your post, there aren't universal meanings of the words "model" or "theory" among scientists. It isn't surprising that sometimes scientists and non-scientists alike may call a highly speculative idea a theory, given that both groups of people are drawn from the same population. So naturally you wouldn't (and didn't) claim that your own definitions represent those of the scientific community in general. But that's fine, since your goal as I understood it was to explain what YOU mean when you speak of theories and models.

I would probably propose a slightly richer structure for the realm of ideas. It seems like there is a natural progression

observation -> speculation -> hypothesis,

where an observation might come through the senses, finding an inconsistency in an argument or theory, or noticing that there is currently no explanation for something that is not "inherently" unexplainable. Some examples you used as theories I would probably think are hypotheses.

My own understanding of models is that they are devices that capture the outward manifestations of a phenomenon. That is a little different from your definition in that models do not necessarily follow as consequences or examples of a theory. Balmer's formula for the hydrogen spectrum comes to mind as a kind of model where there was no clue or existing theory of its origin. This model stimulated the development of the Bohr atomic model (or, at the time, theory?). On the other hand, calling the Standard Model a model rather than a theory seems like a matter of personal choice, given its extreme success in predicting far more than is put into it as parameters, and having no established deeper theory that explains it; having many parameters reflects that the Standard Model covers a lot of territory.

Quantum field theory by itself is a computational/representational framework rather than a theory (as you know well). There are specific instances of QFTs like those that make up the Standard Model, but attaching the label of "theory" to quantum field theory itself seems a bit generous.

String theory illustrates an interesting case. Calling it a model is inappropriate, since its intended purpose as a fundamental theory is largely rooted in resolving inconsistencies between general relativity and quantum mechanics. Lacking contact with observations that can uniquely test string theory, it might be more appropriate to call string theory a very extensive hypothesis. But that wouldn't really be fair either, since theorists have paid a lot of attention to internal consistency and consistency with established physics. I have read of arguments that it is best to think of string theory as a framework...

In addition to frameworks, there is the role of "principles," e.g., symmetries and equivalence principles, which can be important in theory development. More than mere inputs to a theory, they are powerful ideas that can cut across a variety of phenomena and indicate the correct mathematical framework, but often are underivable from a fundamental theory.

Overall, it seems hard to neatly partition and label the various stages of idea development and their varying degrees of confirmation and robustness...

Sure, as I wrote in the very beginning of my post, this was meant to be a clarification for how I want to use these words. I don't say everybody does or should. I am aware that what I wrote is not what you'd find in the philosophy of science, it is just how I think 'theory' and 'model' are actually used, e.g. in papers I read. That being said, it doesn't matter to me whether you think the word 'theory' is appropriate for 'quantum field theory' or not. Fact is, it is called a theory. Besides, this specific case comes back to what Neil' mentioned in the first comment: in reality things are most often somewhat fuzzy, like e.g. second quantization itself is more or less a working assumption.

You say "It seems like there is a natural progression

observation -> speculation -> hypothesis"

Which sounds good, but I honestly don't think this is actually the case in theoretical physics today. Tell me where all the 'speculations' about unparticles, extra dimensions, time travel, parallel universes, or all other kinds of more or less unmotivated modifications of our theories come from for which we have no observational evidence whatsoever? This question isn't meant rhetorically, I would really like to hear what you think is the reason for this increasing departure from observational evidence?

Yes, I agree, my biggest problem with philosophy is that too much of it seems to be about discussing the meaning of words.

As for whether a theory is true or false, I don't know exactly what you are referring to, but I guess the problem isn't one with scientific theories in particular, but generally the question what is 'truth'. Well, I'm surely not the one going to answer this question, but I think this is not actually the question to ask here. I'd say a theory can provide us with a more or less useful framework for making wrong or right predictions. It allowing us to make useful predictions with high confidence doesn't necessarily imply it is 'true'. Best,

I'm with Lisa. I don't see my job as answering the Why's, but the How's. That doesn't mean I am not interested in the question. Neither do I think one should leave it completely aside, as I generally think a too strict separation of different fields (may that be here e.g. philosophy and science, or possibly sociology?) is undesirable. I just don't think one should spend too much time on questions that are very unlikely to ever be answered as long as there are more important and tangible issues at hand. It's just too easy to lose the way within a forest of why's.

one comes up with what I consider a theory should be minimally limited to be as to what is for a required to do. I find much of modern physics has stepped well beyond this requirement; for they are in some sense seeking phenomena that doesn’t need to be explained, since it is not observed.

Yes, and I would like to ask you the same question that I asked Peter above: why do you think this is the case? I actually think Uncle Al has answered this question above, but I would like to hear your take on it.

One should keep in mind though that it's not necessarily the case that experiment and observation comes first, and theorists go and explain. It can also be the other way 'round: theory comes first, and experimentalists go and confirm. This I would say, is the the dream of every theoretical physicists: making a prediction and being confirmed by experiment, or as you say "they are in some sense seeking phenomena that doesn’t need to be explained, since it is not observed."

“I'm with Lisa. I don't see my job as answering the Why's, but the How's. That doesn't mean I am not interested in the question. Neither do I think one should leave it completely aside, as I generally think a too strict separation of different fields (may that be here e.g. philosophy and science, or possibly sociology?) is undesirable. I just don't think one should spend too much time on questions that are very unlikely to ever be answered as long as there are more important and tangible issues at hand. It's just too easy to lose the way within a forest of why's.”

I can respect that the how’s are of greater relevance and focus and yet from what you said you are not of the same stripe in this regard as Lisa Randall presents herself. As you revealed in your review of Richard Dawkins’ book you measured up by his assessment to being a sexed-up atheist. In terms of the interview and after reading her book, as well as attending a lecture she gave I tend to think you are much sexier in this regard then Ms. Randall :-) As you notice I’ve left a link to that interview so you might render your own opinion.

“Yes, and I would like to ask you the same question that I asked Peter above: why do you think this is the case? I actually think Uncle Al has answered this question above, but I would like to hear your take on it.”

First I must commend you for understanding what I said, for after looking it’s probably the most garbled sentence I’ve ever written:-) The reason I think things are going this way are a little less sinister the dear Uncle would put it. I feel it relates to in effect what I would refer to as a sort of scientific denial. Some of it based on the philosophical trappings of the standard QM perspective as it relates to the ontology of it, coupled with the general perspective that the basic problems lie with the short comings of GR in terms of its overall depth of truth(sorry for this word). Basically I agree with Einstein that we cannot hope to get a handle on the future of physics until we deal with its warts ,as to what they are and what this might reveal in terms of direction. You are probably less sympathetic to this since you are surrounded by many of the foundational stripe at PI both of the QM variety and GR type. So in short I would contend that without this firm footing the theorists are left where we now see them. Einstein expressed this much better then I will ever hope to, when he said:

“It has been often said, and certainly not without justification, that the man of science is a poor philosopher. Why, then, should it not be the right thing for the physicist to let the philosopher to the philosophizing? Such might indeed be the right thing at a time when the physicist believes he has at his disposal a rigid system of fundamental concepts and fundamental laws which are also well established that waves of doubt cannot reach them; but, it cannot be right at a time when the very foundations of physics itself become problematic as they are now. At a time like the present, when experience forces us to seek a newer and more solid foundation, the physicist cannot simply surrender to the philosopher the critical contemplation of the theoretical foundations; for, he himself knows best, and feels more surely where the shoe pinches. In looking for a new foundation he must make clear in his own mind just how far such concepts which he uses are justified, and are necessities.”

So I have come to understand that when the theorists take this in earnest, as to look straight at the issues and not be content “to slumber on their quantum pillows” (as to paraphrase J.S. Bell) we might begin to go in a direction provided by this firmer footing.

Hi Phil, what's a "why" and what's a "how"? I think you'll have to be more specific! For example, when Einstein saw pollen molecules zig-zagging on water, didn't he ask "Why is the pollen behaving like that?" Isn't "why" a scientific question?

I just think we should say that science tries to answer fundamental questions about "why" or "how" the world is like it is - explaining phenomena in terms of more fundamental theories. I think when you say that science "cannot answer the 'why' questions" you are suggesting that we might one day discover a phenomenon which cannot be explained in terms of a more fundamental theory, in which case we will have to say we cannot say "why" the universe is like it is. This idea of yours agrees with Steven Weinberg: "I have to admit that, even when physicists will have gone as far as they can go, when we have a final theory, we will not have a completely satisfying picture of the world, because we will still be left with the question 'why?' Why this theory, rather than some other theory?" - see here.

However, I don't see why we should necessarily get to this "end of the line" - a phenomenon which cannot be explained in terms of a more fundamental theory. Maybe things just go on forever - see the "Tower of Turtles" section on my page It's a Small World. Also, maybe science is capable of revealing a complete "theory of everything". If that theory has no free parameters then we will know "why" the world is as it is. So Lisa Randal said: "We're not going to be able to answer the 'why' questions." If Lisa Randal has already given up on answering the most fundamental questions then that is her prerogative, but that doesn't mean we all have to give up hope.

Tell me where all the 'speculations' about unparticles, extra dimensions, time travel, parallel universes, or all other kinds of more or less unmotivated modifications of our theories come from for which we have no observational evidence whatsoever?

That is a good question, but since I don't claim to have the answers I'll just give my perspective. The question of why we see so much generous speculation can be rephrased as two questions: Why do theorists spend serious effort speculating about issues that we have no reasonable hope of resolving observationally? What produced the environment where these kinds of speculations are considered to be acceptable or even sometimes admirable scientific endeavors, worthy of significant journal space, conference talks, and even a basis for hiring or tenure decisions?

The second question is sociological, but its answer probably has its roots in the answer to the first. One could take a cynical view and dismiss the phenomenon as scientists chasing grant money and tenure by working on the latest fashions. Surely there is some of that, maybe a lot of it, but I think it is too simplistic a view; even if it answers the first question it doesn't seem to address the second. The current situation didn't come about suddenly, but interpreting the past and present is tricky. No worries though; this is a discussion in a blog, so here goes...

Specific examples can be more clear than generalities, so let's consider one line of thinking that leads to parallel universes. When cosmological inflation was first proposed around 1980 to solve problems like that large-scale flatness and isotropy that seem to be present in our universe today, it was quickly realized that the presumed mechanism, a single scalar field that somehow got trapped in metastable false vacuum, should not decay (tunnel) to the ground state "true vacuum" everywhere at the same time; simultaneous tunnelling everywhere throughout a causally disconnected region is very contrived. Alternatively, one could assume some probability of local tunnelling, where each tunnelling event is supposed to lead to a new "bubble universe" that immediately starts to expand into the false vacuum (but which might be eaten by the false vacuum which is also expanding, if it starts out too small); this is more "natural," but then we have to worry about collisions between bubble universes that could occur if some universes expand toward each other faster than spacetime between them expands. We don't see evidence of such past bubble collisions, so they can't be very frequent, and this requires a low tunnelling rate. But assuming a low tunnelling rate comes at a cost: the spacetime in false vacuum continues to expand faster than it tunnels to true vacuum, leading to the idea of eternal inflation. With eternal inflation, new universes keep being generated by tunnelling events, and we arrive at one kind of a parallel universe picture. (To anyone who is familiar with the inflationary picture: please forgive my simplifications; hopefully I have captured the essence, however.)

I think one key point is that the original idea wasn't that we should have many universes. That was an unintentional consequence of another idea (inflation) that had enough theoretical appeal that it was taken seriously (it "explained" certain important but puzzling observations). In conjunction with other important and less speculative cosmological theories/ models/ whatever, inflation offered predictions of certain anisotropies of the cosmic microwave background which were subsequently observed. Thus, inflation is ugly and has seemingly absurd consequences from one standpoint, but it also makes predictions that agree with observation. If one believes that inflation should never stop everywhere, and hence will forever create new universes, then a whole new playground of ideas opens up. Moreover, since this playground is implied by a respectable theory/ model/ whatever then it can inherit some degree of respectability, or at least an attitude of tolerance. Beyond that, the inflation-inspired multiverse can serve an additional purpose: it provides a possible mechanism for "populating" the string theory landscape! Because both string theory and inflation have become mainstream (but speculative) ideas, the synergy between the two multiverse pictures gives parallel universes even more respectability.

Neither unique consequences of string theory nor activities in other universes seem to have much hope of becoming observable (possibly excepting certain kinds of collisions between bubble universes, which in principle could be observable if they left an imprint on the CMB), yet they are taken seriously. What, if anything, has gone wrong?

I think this example illustrates one picture where (my rephrasing of) your question may have an answer: both theoretical interest and sociological acceptability of very speculative ideas can arise when no sensible alternative is known to exist. I personally think there are several sources of trouble. Obviously, speculation is free, and new empirical knowledge that can guide good ideas is in short supply. But I think there are other important factors, too. This post is already way too long, though, so I won't go into them now. Maybe later...

Hi Marty, I just think it's human nature: every scientist would love to be the one that discovers the "Theory of Everything", and parallel universe theories offer a shortcut to achieving this: "Why are the physical constants apparently fine-tuned? The physical constants are set to different random values in each universe. Hence, Theory of Everything. Problem solved."

However, surely it is too soon to be resorting to such shortcuts. As Paul Steinhardt says: "I think it is far too early to be so desperate. This is a dangerous idea that I am simply unwilling to contemplate." - see here.

Yes that’s precisely what I mean, that science should not give up on what are for the most part the small whys? Something like Darwin with “why” is life so diverse and ever changing, answering it is nature’s best method to assure continuance within an ever changing environment. Another being Einstein’s revelation, that it is with the recognition of time being a dimension both equal and indistinguishable from what we call spacial that the effect of energy/matter has on the architecture of this background that accounts for “ why” things move as they do. My favourite of course is more of the philosophical or fundamental bend, when Descartes asked “why” am I certain that I am and realized it is “because I think”.

As for the even greater why’s, as you say they will either be answerable or not as will be discovered. It’s just that in many cases science is setting itself up to first insist that the whys are not only unnecessary for understanding, yet more so that there isn’t any. This of course is only an opinion, which in science should be considered merely a hypothesis. It is however a hypothesis that was first proposed by true scientists (which I am not), which I just happen to agree with.

Thanks for the link to the interview, which I hadn't read before. Well regarding what she says about religion, it goes very well with me. Actually, the very first answer (Later I decided that just doing math would drive me crazy. I'd be up all night working on a problem, and I thought, "I can't live the rest of my life like this." [Laughs] I wanted something more connected to the world.) is funny, I think I must have said essentially the same various times.

You are probably less sympathetic to this since you are surrounded by many of the foundational stripe at PI both of the QM variety and GR type. So in short I would contend that without this firm footing the theorists are left where we now see them.

I am sympathetic to what you say, and I am indeed afraid that for this reason part of the field I work in develops into self-referential bubbles of nothing (I'd actually say this is already the case). However, there has been over the last years a strong trend towards putting more emphasis on the phenomenological side. On the other hand there has also been a trend of those who can't come up with any phenomenological model to argue in their defense with the importance of mathematical investigations. I am afraid that these two trends will at some point split and the middle ground gets lost. See, I come across a lot of 'phenomenological' models that lack 'firm footing' on the theoretical side, and then on the other hand there are the 'theoretical' examinations that lack 'firm footing' on the phenomenological side. One of the reason why this happens I think is simply one of over-production. There are too many people who produce too much without sorting out what is already there. They specialize in some area, will be convinced they are doing the only right thing, but this fragmentation will never result in any convergence - which was badly needed exactly because the experimental situation is difficult. The reason why this doesn't happen, so I think, is simply that no matter what it would be to the disadvantage of many people, so there are no incentives to sort out. This should be done by 'Nature' (i.e. falsifying varios approaches by evidence) and this lacking selection process is a problem that one has to deal with some way (I mentioned this as the 'measurement problem' in this earlier post).

Andrew: regarding the why and the how. What I mean is answering a question without providing a mechanism (the 'how') isn't sufficient. I could tell you I think the parameters of the standard model are what they are because they maximize complexity, that's an answer to the 'why' but that's not sufficient, because the 'how' isn't clarified. To make this a scientifically useful approach one would have to explain 'how' come the parameters get the values they have. Best,B.

I just think it's human nature: every scientist would love to be the one that discovers the "Theory of Everything", and parallel universe theories offer a shortcut to achieving this

You are probably right that this motivates some people. But there are plenty of people working on very speculative ideas which have no hope of having a huge impact. I heard a conference talk within the last month which was so far out, so speculative, and so inherently impossible to ever make contact with observation that I was amazed that anyone would want to spend their time on something like that, much less publicly talk about it in front of other scientists. That idea won't be making anyone famous...

Even if the search for fame were a major factor in why people work on very speculative but untestable ideas, it still doesn't say anything about what created the environment where such activity can become mainstream science. I think the full explanation is probably more complicated...

I agree with Marty. It's more complicated than people just wanting to be the first to find the TOE. That I could understand. There are many people who know damned well what they do is so far off reality or the possibility to ever be testable in their lifetime (and longer) is basically non-existent that there has to be some other reason. Part of this I think is just because they like their job, its fun, and somebody pays them.

But more than that: given that these speculation are interesting, and have an entertainment value not unlike various forms of art, they serve as an inspiration at the very least for Science Fiction writers, or pop-sci magazines. People just like to read weird things, and to put it this way: there is a market. A priory, I actually don't have any problem with that, wouldn't it be that money that goes into X isn't there for Y - and this trend goes on the expenses of 'real' science. It might sound a bit weird, but the situation isn't so unlike to what happens on the financial market. Lots of speculations, advertisements, bubbles of nothing with no 'real' backup that have to burst sooner or later. I don't think this similarity is coincidentally, it's a consequence of the feedback and selection mechanism that our community provides, and I think it needs a makeover. Best,

A very interesting point about string theory is its "uplifting" from a theory of mesons to a theory of Planck scale. Such radical change does not fit in the scenary of the post, where a theory seems to be linked to specific phenomena to be explained.

I’m glad you found the article of interest. I guess I have subscribed to Discover since it came out and although it’s not intended to give one an in depth understanding of anything, it does serve quite well as say the news magazine of science. You say you agree with Lisa on the religious aspect of things, which I suspect you would. What I was more referring to was the why aspect that was attached to the question and her response. I have the feeling she excludes all why questions as being of any utility. On the other hand I have come to understand you are not the same in this regard. I would suspect it could relate to the rock climbing persona as apposed to artistic one. When I read Warped Passages she related pretty well her passion for science, yet I was left to feel this didn’t have outlets in terms of her other interests. Although she did try to use analogy to clarify some points, I found them strained and a little contrived. In contrast to this you have Brian Greene who’s use of analogy and humor had me come away feeling he was the Mark Twain version of a physicist. He almost had me falling for string theory:-) Don’t take me wrong, this is not intended as a slight, simply my personal observation of contrasts of characters and how it may translate in ones work in relation to outlook.

I did find out that I was wrong on your take on the foundations, as they relate to physics and the base from which theory is built. To be truthful in the last several years I pay more attention to this then most other aspect of the discipline. Partially because of my own personal slant and yet I would also have to admit being not able to cope with all the mathematical structure of the current approaches. That’s not to say I don’t try to gain some sort of an overview. To serve as a crude analogy, I have always felt that the foundations to the likes of Einstein, Bell and a few others, served as sort of a conscious for their practice of the discipline. I find may theorists today consider that to admit to holding such notions as almost an embarrassment. I am also convinced that this also serves to be a major stumbling block for many. To draw a philosophic parallel, Socrates said “the unexamined life is not worth living”. I understand that what Einstein and others have attempted to remind and caution their peers is that “the unexamined foundations, leaves the science not worth pursuing”.

Often overlooked and misused is that when believers in a phenomenon have a bad (or seemingly bad) explanatory theory, it doesn't really cast doubt on the phenomenon. For example, traditional practitioners of acupuncture had "strange" theories of why it worked. That instinctively leads us to doubt the efficacy, but consider: Suppose that somehow, it is found that a certain practice works. The practitioners may come up with a totally absurd theory to explain why. That is apparently what happened with accupuncture, which AFAIK has been shown to have a moderate efficacy in many ways (maybe not in all ways claimed by ardent proponents!)

It just doesn't follow from the suspect theory to doubt the phenomenon, but doubting it is the tempting psychological reflex in such cases.

I don't understand this. Suppose you install some kind of dictatorship which declares that no leading journal will ever again accept a paper on [insert name of field that you don't like HERE]. Do you really think that this will benefit "real" science, whatever that is? How *exactly* is that going to work?

Put it another way: suppose that all this speculative work had never been done. How would we benefit? Would we have a computation of the electron mass from first principles by now? Or what?

Here I am stressing the practical aspect, and leaving to one side the *extremely* dubious moral aspect of forcing people to avoid certain subjects --- which, whether you realise it or not, is what you are proposing here.

It is nice to see the train of thought commentors are leaving for consideration.

Bee,

I am having trouble digesting your "mind map." So many words your using, it leaves a certain ambiguity with what you are actually saying. Could be my denseness.:)

Can you "map" how you would have assigned "model" "theory" "Hypothesis." I would think this would be much more "clear and concise," as a toy model perhaps?:) The different ways it could be used.

Feynman was able to see and decipher the context of the interactions visually, so he needed "a method to record." He was gifted as Dirac was in terms of visualizing and applying a method. I am guessing Feynman learnt this trick from Dirac, but was also very capable himself.

I tried to capture this with Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe"

While not of the ilk of some of these commentors and their credentials, I was struggling to make sense of "the order."

“It just doesn't follow from the suspect theory to doubt the phenomenon, but doubting it is the tempting psychological reflex in such cases.”

Yes, the theory that the moon is made of cheese, does not disprove the existence of the moon; and yet the moon being real lends no validity or significance to cheese. On the other hand, if the cheese it required to have the moon to be real, then neither has meaning as it would relate to proof.

Deduction requires more then simply a premise to be sound; for it requires the premise to be self evident or deduced from one already shown to be. Further the deductive statement made must be a strong one, as to establish an actual commonality to which it is connected.

You completely, totally, utterly misunderstand me. I know you've been following this blog for a longer time so by now you should have realized that what you say has nothing to do with what I think. What I am saying is that for science that is as speculative as ours to work optimally there should ideally not be external influence of any kind, but this *is* de facto the case. The way the selection of topics, support of researchers, incentives generally are funtioning today, and are allowed to affect the people working in the field, it *does* influence what people work on, and it *does* also influence how people present/advertise their work. What concerns me is that I know a lot of people who have told me they are working on X because that's what they get the grant for and where the money is, or where they could get a job, but they'd actually rather work on Y. This is the problem. The idea that one can use marketplace tactics in fundamental research, and direct people's interest by supporting selected areas but not others - in a field where there is, potentially for decades, no 'real' value, where the only judgement we have is that of our own community - is completely mislead. The only thing it does is that it distorts the objectivity of our opinions, which further worsens the situation - that's what I mean with 'bubbles of nothing'. Best,

Yes, from what I gather I'd say I am more philosophically inclined than Lisa, but hard to say since I don't know her (I am never sure how accurate the public profile of a person actually is.) I liked her book better than Greene's though. I think I never finished the latter. (I'm not actually entirely sure why since Greene's was without doubt better written. It just left me with a feeling of artificiality, whereas Lisa's book seemed somewhat more 'real'.) Best,

While one can learn to draw using "pre" in the blog entires, such drawings I linked too, in my earlier picture reference of "When is a pipe a Pipe?" can often be used like mind maps to illustrate a method of seeing. Why I used that pre text to draw the way I was seeing it , that I am asking you if you can summarize this whole blog entry into such a diagram? John Baez is familiar with such a method of using the keyboard to draw.

I know your busy.:) Do you understand now? Why the mathematical structure of the universe is such an "elemental way" of trying to describe nature in the way many of the constants of nature of are looked for?

In terms of drawing in html with key board. make sure you use greater and less signs then beside the br signs. I had to removerthe brackets because this blog format in comments will not allow br in them.

Well, even after re-reading your comments I am sorry, but I still don't understand your question. The essential content of the post is what the figures show that I've included, the rest is plenty of examples. If even these figures are too much, then how about mind-mapping it as

Real World out There ---- [Theory] ----> Model

That's it. The only thing I've been trying to say in this post is that I see a theory as a procedure to map the real world to a specific model. You could also write it this way:

Theory: RWOT -> Model

The model you obtain this way doesn't contain all the information, it will typically only contain certain aspects that you're interested in, I'd go so far to say there is no perfect one-to-one map. E.g. if you have a bag of hydrogen gas, you could map an atom using quantum mechanics to understand the energy levels, or the whole bag using thermodynamics, and use the 'model' of an ideal gas. Hope that helps,

Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition.

My central Theme on my blog site is on "How theories are born in mind?" This is most certainly an aspect of the self that looks at all th information and forms a method to the approach and how vast this information to have reduced it to such a theory?

In 1952, in his book Relativity, in discussing Minkowski's Space World interpretation of his theory of relativity, Einstein writes:

Since there exist in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence. Albert Einstein

While Einstein looked at the four dimensional aspect of our reality this step was lead too, after careful deliberation. Yet, there are those who say that this aspect of determination holds a perceptive that is reducible from something much more vast in it's consideration. Then, we say that Einstein's view is a "result of?"

We could not have gotten there if it were not for a geometrical progression, yet, we are now lacking in "this determination" and method by relegating anything beyond the spacetime and our views about quantum mechanics and question the foundation aspects.

It forced people to contend with the directions they had to go. Pi one direction while that other is well understood in terms of the approach Pi Institute speaks of in terms of Quantum Gravity.

I have gone on to long. Hopefully the point is understood that I asked of you while only a elementary idea in terms of the approach of theoretics, it had to have a basis in it's formalization and a mapping of the intricacies.

It had to be pushed back even more as we look at the microseconds of this universe? It's anew cosmological view of the universe and once this is accepted, then one realizes the depth of perception that is being garnered.

Setting aside our differences in the appropriate use of "model" and "theory", all the concepts; idea, speculation, hypothesis, theory and law of nature are conceptual sketches that our minds put together, usually out of words and/or symbols, to try to communicate something about a sensory perception, or a set of sensory perceptions 'of reality' to others.

By their natures, they're all incomplete, and therefore, at best, we can not be surprised if, although 'verifiable with some degree of confidence' by repeated observations of 'one kind', they may fail to provide confident 'predictions' in some other 'area'.

In summary, in the limit, neither reductionism nor emergence can be assured because of incompleteness. And science probably remains open-ended forever.

This was essentially your conclusion as well. But this is a more direct route :-)